Make the jerk rub by combining the salt, allspice, brown sugar, onion powder, garlic, nutmeg, pepper, ginger, cayenne pepper, cinnamon, & thyme. Toss the chicken pieces with the spice mixture, then cover & marinate in the refrigerator 2 to 4 hours.
Preheat the oven to 350 degrees F. Pour the vegetable oil into a 9×13 inch baking dish.
Place the chicken pieces skin-side up into the baking dish. Bake in the preheated oven for 1 hour 20 minutes, until no longer pink near the bone. Turn the oven on to broil, & cook until the skin crisps, 2 to 5 minutes.